Robert has a collection of 26 fishing lures and Lucy has a collection of 34 fishing lures. Robert is adding 4 new lures per month to his collection, while Lucy is adding 2 new lures per month to her collection. After how many months will Robert and Lucy have the same number of fishing lures? Write and solve a system of equations.(1 point)
Responses
2 months
2 months
4 months
4 months
11 months
11 months
18 months
Let's represent the number of months as x.
Robert's collection is initially 26 lures and he adds 4 lures per month, so the total number of lures Robert has after x months is 26 + 4x.
Lucy's collection is initially 34 lures and she adds 2 lures per month, so the total number of lures Lucy has after x months is 34 + 2x.
To find when Robert and Lucy will have the same number of lures, we set their total number of lures equal to each other:
26 + 4x = 34 + 2x
Subtract 2x from both sides:
2x = 8
Divide both sides by 2:
x = 4
After 4 months, Robert and Lucy will have the same number of fishing lures.